Yes, a low carb and low calorie diet (if she's not getting enough fat or protein to make up for the low carbs) could produce ketones in the urine.
It could be normal and it could also be a sign of other metabolic issue. Some basic blood tests to rule out diabetes would be prudent and not too expensive.
Does she have any other symptoms of diabetes?
If not, then there may not be any problem.
In the diet program called UltraLite that I use here, we have patients do a first morning urine test strip to check and make sure they are in a mild state of ketosis. This is a low-carb and generally low-calorie diet, so it may be similar to what she has been doing. If she's been active and on too few calories, that could all explain the fatigue and ketones, but better to be sure nothing worse is going on.
Hope that helps.